L1 Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent

In this work, we study the following nonlinear homogeneous Neumann boundary value problemβ （u） -diva （x, 7u） f in fΩ, a （x, u）. η= 0 on Ω, where Ω is a smooth bounded open domain in RN, N ≥ 3 with smooth boundary Ωand ηthe outer unit normal vector on Ω . We prove the existence and uniqueness of an entropy solution for L1-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.